"I was queen of my senior prom. I probably only won because I was on the prom committee. I wore hoops and petticoats to make sure my princess gown stuck straight out—it had to be big, big, beyond bouffant big!"

In July, father John McCain was diagnosed with stage 4 glioblastoma, an aggressive form of brain cancer, which also claimed Beau's life.

When the 33-year-old began crying, the politician went over and consoled her, adding:

"There is hope... And if anybody can make it, your dad [can]."

Biden is also optimistic about "breakthroughs that are occurring now," regarding potential treatment options and cures.

"There's a lot of things happening. Any of you who have somebody who is diagnosed with gliobastoma, which is about as bad as it gets, there's breakthroughs that are occurring now... And it can happen tomorrow."